Treeby, Bradley*
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Accurately representing acoustic source distributions is an important part of ultrasound simulation. This is challenging for grid-based collocation methods when such distributions do not coincide with the grid points, for instance when the source is a curved, two-dimensional surface embedded in a three-dimensional domain. Typically, grid points close to the source surface are defined as source points, but this can result in "staircasing" and substantial errors in the resulting acoustic fields. This paper describes a technique for accurately representing arbitrary source distributions within Fourier collocation methods. The method works by applying a discrete, band-limiting convolution operator to the continuous source distribution, after which source grid weights can be generated. This allows arbitrarily shaped sources, for example, focused bowls and circular pistons, to be defined on the grid without staircasing errors. The technique is examined through simulations of a range of ultrasound sources, and comparisons with analytical solutions show excellent accuracy and convergence rates. Extensions of the technique are also discussed, including application to initial value problems, distributed sensors, and moving sources.
- Publikační typ
- časopisecké články MeSH
Non-invasive, focal neurostimulation with ultrasound is a potentially powerful neuroscientific tool that requires effective transcranial focusing of ultrasound to develop. Time-reversal (TR) focusing using numerical simulations of transcranial ultrasound propagation can correct for the effect of the skull, but relies on accurate simulations. Here, focusing requirements for ultrasonic neurostimulation are established through a review of previously employed ultrasonic parameters, and consideration of deep brain targets. The specific limitations of finite-difference time domain (FDTD) and k-space corrected pseudospectral time domain (PSTD) schemes are tested numerically to establish the spatial points per wavelength and temporal points per period needed to achieve the desired accuracy while minimizing the computational burden. These criteria are confirmed through convergence testing of a fully simulated TR protocol using a virtual skull. The k-space PSTD scheme performed as well as, or better than, the widely used FDTD scheme across all individual error tests and in the convergence of large scale models, recommending it for use in simulated TR. Staircasing was shown to be the most serious source of error. Convergence testing indicated that higher sampling is required to achieve fine control of the pressure amplitude at the target than is needed for accurate spatial targeting.
A full-wave model for nonlinear ultrasound propagation through a heterogeneous and absorbing medium in an axisymmetric coordinate system is developed. The model equations are solved using a nonstandard or k-space pseudospectral time domain method. Spatial gradients in the axial direction are calculated using the Fourier collocation spectral method, and spatial gradients in the radial direction are calculated using discrete trigonometric transforms. Time integration is performed using a k-space corrected finite difference scheme. This scheme is exact for plane waves propagating linearly in the axial direction in a homogeneous and lossless medium and significantly reduces numerical dispersion in the more general case. The implementation of the model is described, and performance benchmarks are given for a range of grid sizes. The model is validated by comparison with several analytical solutions. This includes one-dimensional absorption and nonlinearity, the pressure field generated by plane-piston and bowl transducers, and the scattering of a plane wave by a sphere. The general utility of the model is then demonstrated by simulating nonlinear transcranial ultrasound using a simplified head model.
- Publikační typ
- časopisecké články MeSH
PURPOSE: Transurethral ultrasound therapy is an investigational treatment modality which could potentially be used for the localized treatment of prostate cancer. One of the limiting factors of this therapy is prostatic calcifications. These attenuate and reflect ultrasound and thus reduce the efficacy of the heating. The aim of this study is to investigate how prostatic calcifications affect therapeutic efficacy, and to identify the best sonication strategy when calcifications are present. METHODS: Realistic computational models were used on clinical patient data in order to simulate different therapeutic situations with naturally occurring calcifications as well as artificial calcifications of different sizes (1-10 mm) and distances (5-15 mm). Furthermore, different sonication strategies were tested in order to deliver therapy to the untreated tissue regions behind the calcifications. RESULTS: The presence of calcifications in front of the ultrasound field was found to increase the peak pressure by 100% on average while the maximum temperature only rose by 9% during a 20-s sonication. Losses in ultrasound energy were due to the relatively large acoustic impedance mismatch between the prostate tissue and the calcifications (1.63 vs 3.20 MRayl) and high attenuation coefficient (0.78 vs 2.64 dB/MHz1.1 /cm), which together left untreated tissue regions behind the calcifications. In addition, elevated temperatures were seen in the region between the transducer and the calcifications. Lower sonication frequencies (1-4 MHz) were not able to penetrate through the calcifications effectively, but longer sonication durations (20-60 s) with selective transducer elements were effective in treating the tissue regions behind the calcifications. CONCLUSIONS: Prostatic calcifications limit the reach of therapeutic ultrasound treatment due to reflections and attenuation. The tissue regions behind the calcifications can possibly be treated using longer sonication durations combined with proper transducer element selection. However, caution should be taken with calcifications located close to sensitive organs such as the urethra, bladder neck, or rectal wall.
Computational models of acoustic wave propagation are frequently used in transcranial ultrasound therapy, for example, to calculate the intracranial pressure field or to calculate phase delays to correct for skull distortions. To allow intercomparison between the different modeling tools and techniques used by the community, an international working group was convened to formulate a set of numerical benchmarks. Here, these benchmarks are presented, along with intercomparison results. Nine different benchmarks of increasing geometric complexity are defined. These include a single-layer planar bone immersed in water, a multi-layer bone, and a whole skull. Two transducer configurations are considered (a focused bowl and a plane piston operating at 500 kHz), giving a total of 18 permutations of the benchmarks. Eleven different modeling tools are used to compute the benchmark results. The models span a wide range of numerical techniques, including the finite-difference time-domain method, angular spectrum method, pseudospectral method, boundary-element method, and spectral-element method. Good agreement is found between the models, particularly for the position, size, and magnitude of the acoustic focus within the skull. When comparing results for each model with every other model in a cross-comparison, the median values for each benchmark for the difference in focal pressure and position are less than 10% and 1 mm, respectively. The benchmark definitions, model results, and intercomparison codes are freely available to facilitate further comparisons.
